KAZZY SINGLE

Fast download [Kazzy_Do That Thing].

Good day y'all. Here is an official single by KAZZY.

This is a very cool music with confirm lyrics, I updated my playlist with this sweet music and I've put it on replay.

You too should hear this song out,it'll blow your mind.

Kindly download this good music below!!!!!!

DOWNLOAD HERE!!!!

KAZZY SINGLE

By: busytimeweb on: August 03, 2019

How to Get Rid of Dry Hair and Dry Scalp Updated: August 03, 2019 | References Having dry hair and scalp can be frustrating, but you may be able to find relief! While dry hair and scalp have several causes, changing your hair care habits and using deep conditioning treatments will usually help fix it. To get rid of your dry hair and scalp, adjust your hair care routine to avoid products and techniques that cause dryness. Then, restore moisture to your hair and scalp using a home treatment. Finally, protect your hair to keep it as healthy as possible. Method One of Three: Adjusting Your Hair Care Habits 1 Shampoo your hair no more than 2-3 times a week. Washing your hair too often can dry out both your scalp and hair. You don’t need to wash your hair every day, and skipping washes may help improve the look and feel of your hair. For best results, wash your hair just 2-3 times per week.[1] If your hair feels very dirty, try using dry shampoo between washes. It’s okay to condition your hair between washes, if you like. Tip: Use warm or cool water to wash and rinse your hair, as hot water can dry it out. For your final rinse, always use cool water because it seals your cuticles, which makes your hair smooth and shiny. 2 Use a sulfate-free, moisturizing shampoo and conditioner. Sulfate can dry out both your hair and your scalp, so skip products that contain it. Check the label on your shampoo and conditioner to make sure they are sulfate-free and are moisturizing. This can help you find relief.[2] Variation: If your scalp is also itchy and flaky, you may have dandruff. Switch to a dandruff shampoo to see if it relieves your dry scalp.[3] 3 Condition your hair daily, but avoid your scalp. Using a moisturizing conditioner may help treat your dry hair. Apply the conditioner starting at your ends, then stop just before you reach your scalp. Let the conditioner sit on your hair for 3 minutes before rinsing it out with cool water, which seals your cuticle.[4] Don’t put the conditioner on your scalp because it may worsen the dryness, especially if you have dandruff. 4 Do a 20-30 minute deep conditioning treatment once a week. Apply a deep conditioning treatment to your hair starting at the ends and working up to your roots. Let it sit for up to 30 minutes, then rinse with cool water to seal your cuticle. This will help restore your hair’s moisture.[5] Follow the directions on your product label. 5 Use heat styling tools no more than 1-2 times a week to prevent damage. Unfortunately, styling tools can damage your hair and even cause breakage. Avoid using heat to style your hair if you can. Otherwise, limit your use of heat styling tools to just 1-2 times a week. This includes your hair dryer, straightener, and curling iron.[6] When you do use heat styling tools, apply a heat protectant to your hair first. This will help reduce the damage. Method Two of Three: Using Home Treatments 1 Apply coconut oil to your hair and scalp for 20-30 minutes. Divide your hair into 4-6 sections, depending on how thick your hair is. Starting with the first section, use your fingers to apply a thin layer of coconut oil to your hair and scalp. Continue applying the oil to each section until your hair is coated. Then, cover your head with a shower cap and a hot towel. Let the oil sit for up to 30 minutes, then shampoo and condition your hair to remove it.[7] If you don’t have much time, leave the oil on your hair for 10 minutes. It won’t be quite as effective, but you should see results. Variation: For very dry hair, it’s okay to leave the mask on your hair for longer. In fact, you can even use it as an overnight treatment. Apply the oil before bed, then sleep with the shower cap and towel on your head. Wash your hair in the morning to remove the oil. 2 Do a hot oil treatment to add moisture to your hair. Pour about .5 cups (120 mL) of oil into a bowl. Heat the oil in a pot of boiling water or the microwave until it feels warm. Massage the oil into your hair and scalp, then cover your hair with a shower cap and a warm towel. Let the oil sit for 30-45 minutes. Finally, shampoo and condition your hair to remove the oil.[8] You can use any oil that you have on hand. Avocado oil is a great option for dry hair, and jojoba oil helps with dandruff. You can also use coconut oil, which is great for all hair types. 3 Try a homemade egg yolk mask, which may help with dryness. To make your mask, put 2-3 whole eggs into a clean bowl and add 2-3 drops of lemon juice. Beat the eggs until they get frothy, then apply the mask to your hair using your fingers. Cover your hair with a shower cap and let the mask sit for 20 minutes. Rinse the mask out with cool water, then shampoo and condition your hair.[9] You can use this treatment once or twice a month. Don’t rinse the mask out with warm or hot water because the egg will start to cook and will be harder to remove. Variation: You can add half a banana, 2 tablespoons (30 mL) of honey, 2 tablespoons (30 mL) of olive oil, or 2 tablespoons (30 mL) of coconut oil to your mask for extra softness and shine. However, keep in mind that these ingredients don’t work the same way for everyone and aren’t guaranteed to help your hair. 4 Use a homemade gelatin mask for smooth, shiny hair. Stir 1 tbsp (9 g) of gelatin into 1 cup (240 mL) of warm water. Let the gelatin sit for 5 minutes, then add 1 teaspoon (4.9 mL) of apple cider vinegar and 6 drops of rosemary essential oil. Mix the ingredients, then apply the mask to your hair. Let is sit for 10 minutes before shampooing and conditioning your hair.[10] Instead of the rosemary essential oil, you can use clary sage, lavender, or jasmine essential oil. 5 Apply a thick layer of mayonnaise to your hair to restore moisture. Wet your hair with warm water before applying the mask. Use your fingers to apply a thin coat of mayonnaise to your hair, starting at your ends and working up to your roots. Cover your hair with a shower cap and let the mayonnaise sit for 30 minutes to an hour. Finally, rinse out the mayonnaise, shampoo, and condition.[11] Choose a mayonnaise that contains eggs and oil, as these are the ingredients that treat the dryness. 6 Use an avocado mask to add moisture to your hair and scalp. Add a ripe avocado, 2 tablespoons (30 mL) of extra virgin olive oil, and 1 teaspoon (4.9 mL) of honey to a blender, food processor, or clean bowl. Mix the ingredients together until your mask is an even consistency. Apply the mask to dry hair and massage it into your scalp. Cover your hair with a shower cap and let the mask sit for 30 minutes. Finally, rinse your hair out with cool water, then shampoo and condition.[12] Avocados are rich in vitamins, minerals, and natural oils, so they may make your hair soft, glossy, and moisturized. 7 Use honey to make a deep conditioning mask. For an easy option, mix 1 part honey and 2 parts conditioner together. Alternatively, mix 4 tablespoons (59 mL) of extra virgin olive oil, 2 tablespoons (30 mL) of pure vegetable glycerin, and 2 tablespoons (30 mL) of pure honey to make a mask. Apply the conditioner to your hair and let it sit for 10 minutes before rinsing your hair with cool water.[13] Be aware that honey can lighten your hair. Method Three of Three: Protecting Your Hair and Scalp 1 Eat a nutritious diet or take a multivitamin to avoid vitamin deficiencies. Consuming nutritious foods will help you get the nutrients you need for healthy hair. If you want to use supplements, check with your doctor first to make sure they’re safe for you to take. Here are some ways you can improve your diet to help relieve your dry hair:[14] Eat more fatty fish, like tuna, salmon, sardines, and mackerel. Choose more fresh produce, especially blueberries, broccoli, and tomatoes. Add nutrient-dense foods like walnuts, kidney beans, and oysters. Take supplements for Omega-3s, vitamin A, vitamin C, biotin, and iron. 2 Wear a hat when you’re out in the sun. Sun exposure can dry out your hair and scalp, so spending time outdoors can make your condition worse. Covering your head with a hat helps block the sun’s rays, so it may help with your dry hair and scalp. Choose a hat with a brim for the best coverage.[15] If you can, spend less time outdoors during the sunny parts of the day. 3 Wear a swim cap while swimming to protect your hair from chlorine. Exposing your hair and scalp to chlorinated water may dry them out. Fortunately, you don’t have to give up swimming! Instead, cover your head with a swim cap before you get in the pool. This will protect both your hair and scalp, which may help with your dryness.[16] You can buy a swim cap online. As another option, keep your hair out of the water while you’re spending time in a pool. Community Q&A Question Will hair dye dry out my hair? Community Answer Regular dye will, yes. Henna is an alternative that shouldn't dry out your hair. Question Why do I get dandruff when I brush my hair after a shower? Community Answer It might be that your scalp is not totally clean. Try massaging it for at least three minutes with shampoo. Also, use a clean comb, change your pillow cover every two days and don't brush your hair right after showering, as that is when it is at its weakest. You can also try applying hot oil therapy once a week. Question Can having dry scalp cause itchiness? Community Answer Yes. Question What do I do if I break out in little bumps every time I wash my hair? Community Answer Please describe the problem more specifically. Are the bumps on your head? If so, that's unusual and you might want to try either switching products or seeing a dermatologist. If you're referring to breakouts on your face, you may also consider switching products, or, if you don't already, wash your face with a facial cleanser after you've washed your hair to remove any shampoo/conditioner residue that might be on your skin. If you're just referring to goosebumps on your body, those are totally normal and harmless, and usually occur when you're cold. Question Does using flat irons slow hair growth? Community Answer No, it does not stop hair from growing. However, the flat iron may burn your hair, and you may need to trim your dead ends. If this happens, your hair will not get a chance to get too long. Question I've tried everything possible for my extreme dry scalp, but nothing seems to work. What more can I do? Community Answer Drink lots of water, and try to avoid sugary drinks. Your dry scalp may also be genetic, something you are born with. If this is the case, consider seeking the advice of a dermatologist; he or she will suggest a specially-formulated/medical shampoo and conditioner for you to try. Question Can I use almond oil as a hot oil treatment? Community Answer Yes. You can use coconut, almond, olive, castor or grape seed oil. Question Should I condition my hair after I apply warm coconut oil, though my hair remains oily? Community Answer After using coconut oil, wash your hair with a small amount of shampoo, rinse thoroughly, then shampoo again to ensure the bulk of the oil is gone. Remember to only shampoo on the top of your head, rather than the ends - the suds will take care of the ends. Conditioner is not necessary. Question Are dandruff and a dry scalp the same? If not, what's the difference, and how can I tell if I have either? Community Answer No. Dandruff is a fungal infection, dry scalp is usually white and dandruff would be other colors such as yellow. Question Can becoming bald get rid of small pimples and extreme dryness? Community Answer No, the dryness and acne will stay because it is on your scalp, not your hair. Tips Always visit a dermatologist or your doctor if you are experiencing scalp problems.[17] Warnings Don’t use baking soda treatments if you have dry hair or scalp because baking soda is too harsh and drying. It will likely make your dryness worse.[18] Related wikiHows How to Care For Unmanageable Hair How to Brush Your Hair How to Straighten Your Hair How to Style Preppy Hair How to Deal with a Scalp Sunburn How to Moisturize Your Scalp How to Treat Seborrheic Dermatitis on Your Face How to Clean Your Scalp How to Treat Scalp Pimples How to Treat an Oily Scalp and Dry Roots How to Get a Healthy Scalp How to Make Your Scalp Stop Itching How to Treat Scalp Ringworm How to Get Rid of an Itchy Scalp About This Article Co-Authored By: wikiHow Staff Editor This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. Together, they cited information from 18 references. wikiHow's Content Management Team carefully monitors the work from our editorial staff to ensure that each article meets our high standards. Co-authors: 66 Updated: July 31, 2019 Views: 2,423,619 Article Rating: 80% - 15 votes Categories: Featured Articles | Scalp Health Article Summary References ↑https://www.elle.com/beauty/hair/a24736798/dry-scalp-treatment-remedies/ ↑https://www.elle.com/beauty/hair/a24736798/dry-scalp-treatment-remedies/ ↑https://www.aad.org/public/diseases/hair-and-scalp-problems/scalp-itch ↑https://www.medicalnewstoday.com/articles/320988.php ↑https://www.prevention.com/beauty/a20516469/solutions-for-dry-hair/ ↑https://www.prevention.com/beauty/a20516469/solutions-for-dry-hair/ ↑https://www.liveabout.com/coconut-oil-hair-treatment-3517796 ↑https://www.medicalnewstoday.com/articles/321850.php ↑https://www.medicalnewstoday.com/articles/321971.php More References Reader Success Stories SD Sandra White Christopher Dpc "Because I have a great passion for healthy hair and with the water's being so hard hear in Louisiana I try to help..." more Rated this article: More reader stories Did this article help you? 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Dedicated To Iju Ishaga

IJU ISHAGA MIXTAPE (2019)

Presenting Iju Connect with DJ phenomenal.

Good day y'all, first I wanna thank y'all for responding to my site, as at now I have about 681 page views tho it's small but still ok and to show a sigh of gratitude, I will make a DJ mixtape of artists in iju Ishaga cuz they are the ones(most) that made me achieve that page view.

Now,if you want me to make a mixtape for upcoming artists in your community, all you have to do is follow the site and type your location in the Comment box below.

Please share this to every artist you know in Iju Ishaga and those artist can WhatsApp me on 09024809382 so I can get their music to mix.

IJU ISHAGA WA O!!!!

Countdown begins.

COUNTDOWN

Dedicated To Iju Ishaga

By: busytimeweb on: August 01, 2019

NOTICE!!!!!!!

ATTENTION ⚠️⚠️⚠️

Good day everyone, how y'all doing.

Just wanna inform you on the changes made on the site.

People have been complaining about the arrangements of the story "wrestle of love" so we have made some changes in order to ensure easy navigation for our users.

To view more content(eg the story page), click on more beside the HOME and MUSIC icon above then you can access the story page/ other pages.

We say thank you to those that have invited more audience to the site and we want those who have not to please invite your friends even parents because there are some things they would like to read in the "EDUCATIVE" icon.

THANK YOU! 

NOTICE!!!!!!!

By: busytimeweb on: July 30, 2019

THE POWER OF PHILOSOPHY.

THE POWER OF PHYLOSOPHY

(visual ideology)

Author:-Kolawole Alade & Kolawole Tosin.

NOTE- This is not intended only on Africans alone but everyman kind, who chooses this avenue as an opportunity to upgrade his mental position to archieve a certain height in life .Life is a state (position),lets increase our state in life. As we endeavor this,so our soul(spirit) elevates. This manifest our positions in this coco-world (physical world). REALITY OF LIFE.


I am an African, it is high time we regulate our ideology visually and filtrate the bad philosophy from the good ones.Philosophy is the huge factor that drives a society(either forward or backward). If you are privileged to encounter my medium of orientation on this particular factor that plays a huge role in the state of any society, i urge you to open your minds,accept those views that occur plain to you in harmony and overlook those still struggling to settle in your  minds, keep them aside for the future for you may later adopt it in the future when it comes plain. For example, an adage from African philosophy common in the south western part of Nigeria which are the tribe of the Yorubas quoted as follow,
 
    "TI TENI KAN KOBA BAJE,TENI KAN KOLE DA"

Interpreted as "if somebody space is not tarnished,no room for another man to benefit as a space" another way of interpreting it goes thus,  "if one man success is not tarnished,there will be no space for another man to succeed".  This kind of philosophy negates a society backwardly and causes set back.It indicates an universal insufficiency.It denies an African the power of visions.And creates a huge scenero of awkward competitive atmosphere. Projection of negative insinuations among one another,if an African will have to tarnish an African success believing for him to succeed.So many kinds of negative forces in our atmosphere in Africa that generated out negative perceptions.We created these from imaginations interpreted from negative philosophies.Which sum up to become a powerful force that in turn drives our mindsets in a negative directions that paint our society the way we see it inferiorably to other racial societies.It is known today that African society is far behind in beauty and an Africans hardly see the opportunities around them.

The foreigners are known over recent years to come and take those opportunities from us because they have the power of vision to see those opportunities around us,from the absolute positive evaluation of their philosopies gathered in their mix from time to time. Why we wonder, as we wander among other races in other respective continents.Other race overcome all these challenges technically by re-addressing all these negative ideologies which go a long way in shaping the mental navigation of the people and their environment(development).So philosophy as being neglected by African system to focus on, a tool to develop the society makes Africa far and far behind among other race. A western philosopher quoted that
                       
                                                     "Poverty Is A Mental Illness"....western philosophy

Similarly, i quote that,
                                                                                  "Failure Is A Mental Illness" ,

so it is scientifically understood that words and thoughts are living forces that can never die.All these sum up over years from beginning to drive position of man in life. these sum up to be called "POWER"(GOOD OR BAD POWER, RIGHTEOUS OR EVIL POWER) without exergeration,are result of word content from our "thought force".We live according to our thoughts.So dwell your imaginations on this scope and know more for yourself from your insight.Well no one can lead you right anyway but you can gather scope from people as a fundamental guide.Everyman is a blind entity without the light.And the light is projected from inside you. MAN imagined electric power and it came to past today we are given this idea of producing light for ourselves , this is a miracle.Woooow!!!!!

Meaning that what we think and what we say as made believed resides around  us as a living force over ages of years.This forces constitute to be negative forces(known as evil power by religious entities)which drives a society in a negative direction and positive forces(good power) as claimed by religious entity, which we create over the past years as a result of ignorance around our atmosphere and as we attract it to ourselves by the way we think(thought force) and the way we feel(emotional force).We have the ability to attract because we are "MAGNETIC IN NATURE".This plays a HUGE roll in designing the world we exist in. So lets' turn it right as we reason,think, act,because our instinctive mindS response to these as a command. Your wish is my command ,it says...So what are you commanding(knowingly or unknowingly)? Pay attention to yourself(your mind).Your mind is connected to the celestial and the cosmic world,where all things are made from. Ask yourself why you pray? And where to turn your mind while you pray?
Believe me, if you dare to know,there is always an answer inside you if you concentrate(GOD IS IN YOU) not outside you.Only he need you to concentrate.The outside belongs to the terrestials(what we creates) and they will fade away with time.So mind you,the path to  heaven starts from inside you(your heart).How do you use your heart? A sanctuary of GOD.
                                           
 "GOD visit the heart and observe the feeling of man from his heart"--scriptures
                                                                       
                                                         
                                                                        "Sky is the beginning"--western ideology.

"NATURE".We attract the good and we can attract the bad out of ignorance too.

"what goes forth comes forth" "what goes around comes around", "what goes up comes down"-law of gravity(the law of karma).
                             
                                                          "As ye thinketh so shall ye seeth"-Jesus christ.

So we create our world by the way we feel, see things and think.Because our souls pay heed to our heart and emotions.

WHAT IS YOUR PHILOSOPHY?

What have you made believed by the society,family,peers or by yourself?

take note of these and observe the positive effect and the negative effect of this. Eliminate the negative ones and abide with the positive ones.Further more, develop more positive kinds of philosophy whether from foreign ideology or from your insight(by yourself) so far it will create positive effect by building positive and powerful force around you that will breed positive life experience(good life)

"THINK POSITIVE AND BE POSITIVE" -Kolawole Alade

"what persists, exists"- western philosophy_

means what you think frequently,you are equally creating. lets  create a positive life to live.
Another Yoruba philosophy from where i am from quotes -
"TOBA KOJU SI E KOTA,TOBA KO EYIN SI E KOTA,TI O BA KUN IWO NIKAN KO TUN ERO ARA RE PA" which is interpreted as "IF THE WORLD TURNS POSITIVE TO YOU,MOVE FORWARD(YOU MOVE WITH IT),IF IT'S THE OTHER WAY AROUND,(YOU MOVE BACKWARD)YOU MOVE,ABOVE ALL IF YOU ARE LEFT ALONE,YOU ARE ON YOUR OWN.

This sounds like a game of luck.No confidence as a result of ignorance but i corrected this quoted  above as a lost of confidence(the universe favours the BOLD).
And my quote goes thus,

"THE WORLD TURNS AS WE TURN,MOVES AS WE MOVE .THEREFORE,OUR DESTINATION IS IN OUR HANDS".In similitude  to"HEAVEN HELP THOSE WHO HELP THEMSELVES"-Jesus Christ.

When we help  to turn it right Heaven turn it and when we help to turn it the other way around Heaven turns it too. So lets help ourselves to turn it right,
           
"THINK POSITIVE AND BE POSITIVE"quote by Kolawole Alade.

In my next treat of nature,science based on factual research shows how thoughts work.I title it,

"EVOLUTION OF THOUGHTS"

 This will make you understand how thoughts manifest and materialise as we live.I will say thoughts accumulate,breeding and building a kind of life we wish to live(GOOD OR BAD).
We choose ignorantly or knowingly by thoughts.Accumulation of thoughts over time(FREQUENCY OF THOUGHTS) develop a kind of life we experience in future.See,observe life and understand life.I am giving you just a tip, work hard to observe and understand life because the" Infinite intelligence" is using everything around us to prescribe and describe messages to us,vital messages and He wants you to grasp and understand.People perish because they lack knowledge to understand wisdom and wisdom is the act of acknowledging the mysterious ways of God,the Infinite intelligence.
                                  "SEEK ALL THINGS AND FIND OUT CLEARLY THE TRUTH" -scripture.

To seek is to acknowledge,
                                                               " KNOWLEDGE IS POWER"_Western quote..

Change the mindset nobody thinks you will ever grow,it is based on you to grow or not to, so begin to change all these mindsets,focus on yourself and make the difference.Its not easy to make a change but

        "THINK DIFFERENT AND BE DIFFERENT"- Steve Jobs..


LETS START TO INNOVATE ..........SCIENCE AND TECHNOLOGY.ALL OF THESE CAME FROM WITHIN(MINDSETS).IT IS NOTHING BUT IS A BIG DEAL THAT SWEEP OFF POVERTY.
                                         

My intention is to revive and evolute(develop) our mental state to reflect development in our continental atmosphere.I have a dream as time flies, Africa that   i come from will be of a good image of development in comparism to other continent and other race in other counterpath (like the Western,the Chinese,the United State e.t.c).They develop themselves mentally that reflects the developed state of their society,atmosphere and their environment.So i hereby urge the africa race, it is high time we develop our mental state to see the power of philosophy and visual ideology.Lets begin to picture the African future with unlimited beauty and see the magic of visual ideology.This has been done by the Western society,Chiness society etc and they have seen the magic..So It's Africans turn to boost and boast their conscious minds and focus on the positive waves of the universe to attract to themselves a positive result which is the beauty of life,that will charge our subconscious minds to inspire we Africans in the direction of growth and development.In picture of the European enviroment,Chinese development,American scientific growth,the Japaness technology e.t.c..
In this VOLUME.1 of my writing,i believe that,
                                                                             "YES WE CAN"--Barack Obama

ASPIRATION.

"EVEN THOUGH THE SOLUTION IS STORED IN HEAVEN,THE HEAVEN IS WITHIN OUR REACH (WITHIN US)".
                                                                                        "IT IS IN ME"---Jesus Christ.

                                 
                                 -"Dont let it move you, you move it.Dont let it turn you around,                                                             you turn it around.Be in control of your world"_ kolawole Alade.


Only you knows what you want because only you know your correct and current condition(C.C.C). The question is always before you, what do you want?(NATURAL FACT)
CHECK THIS OUT, the good philosophy to abide with from the south western Nigeria that is the Yoruba tribe quoted:
                                             
                                                  "ONA ABAYO KO SE WA TITI KAWA LO SORUN"
another similar one made believed is
                                        "TERU BA KAN LE TO BA KAN OKE, AMA NIBI AMA GBESI".


Now, these kinds of made believed sounds fundamental but need upgration to improve our mindsets. These quotes meaning in short,that
"EVERY SOLUTION TO EVERY/ANY PROBLEMS(POVERTY,CRISIS,INSECURITIES,UNEMPLOYMENT,UNDEVELOPMENT etc) HAS A SOLUTION "within us" IF CAREFULLLY AND PERSISTENTLY THOUGHT ABOUT IN THE RIGHT AND POSITIVE MANNER,NOT UNTIL WE GO BACK OR VISIT OR JOURNEY TO HEAVEN".

 This proves and boasts the confidence that God himself has wIlled everything to MAN  according to his desire but there is one simple and unconditional condition required from us is KNOWLEDGE(to know) by  seeking,asking,findings,observation,research etc which over the years has been practised by the western region(Europian,Americans )and the Asians of recent(China,Japan,South Korea etc that liften them to self reliance,to build their  individuality and liften their society out of poverty.
WHAT IS CHINA SELLING?- "IDEAS"(Invention and Creativity) and they are making x10 of what Nigeria is making from crude oil and gas. See the miracle, China follow the part of reality,which i am trying to build in the minds of Africans. It is our turn to make the difference awaiting us.
                                             
                                                 "THINK DIFFERENT AND BE DIFFERENT"._Steve Jobs (late and ex CEO of Apple Technology Company).



Steve Jobs created the idea that resulted to a computer being simplified into a mobile phone which we call "ANDRIOD"phone..This is an idea by Steve Jobs,and the idea has resourced to be evaluated as over trillions of dollars so far in the last 20years and created hundreds of millions of jobs and opportunities globally in the last 20years.
                                                                                                           
                                                                  "ASPIRE TO BE INSPIRED"--Western .

MINDS CREATE THINGS LIKE THESE
AND SO MUCH MORE....LETS BE CREATIVE. ACCUMULATION OF THOUGHT FORCES ,PICTURED OUT THESE MATERIALS.(NOT A SECRET BUT REALITY, LETS FACE IT)..


"  'Man Aspires(western philosopher)'. God Inspire"_Kolawole redifine from religious entity which says"FIND AND YOU SHALL FIND(SEE)"_Jesus Christ.

Therefore, Africans let's connect with the dots. This justify what Steve Jobs said in the phrese"Connecting Dot" but he never explain the reality of this, he left it to be a secret for you and i to find out. But he might have imput it to  people around him that use this reality which is made a "SECRET" by ruelity and brutality(a nature of MAN that recides at the outer most part of MAN which oppose the commandment of christ that stated  "LOVE YOUR NEIGHBOR AS YOURSELF". If there is love,there will be no secrets.What is hidden becomes a secret, if not hidden it will not be called a secret but only LOVE can reveal it and free it from captivity.
MAN secrets it but the infinite intelligence knows it all so seek and you shall know!!

WHAT IS YOUR INFINITE INTELLIGENCE?

This means how and who to seek and how can it come to past. That is in you (is atomic part of GOD that is in you , knows all things and it is blessed with atmost power like of GOD that is you yourself in the celestial world where angels are found in the path to the kingdom of GOD.It is equally known by religious entities as the 'SOUL".It has borne so many names according to languages and perceptions to define it.It doesn't matter how anybody sees it but how you see it ,it obeys your wish.
I will advise you to keep visiting this blog busytimeweb.blogspot.com for more findings and details and i assure you that if you do so and dwell in and with it with joy and positivity,you will enjoy a gradual miracle,sighn and wonders as being enjoy by the westerners(Europe, US, Canada,, Austrailia etc.), the eastern asia(China, Japan, South Korea, Hong Kong etc.) and some other individuals in other developing Nations. Be smart to know ,
                "NO DEY DULL AM"_Burna Boy,
                                                   
                                                                 No time "TIME NEVER EXIST"_kolawole Alade.

      Over ages of years from the beginning to this date, MAN has been training, teaching and recreating according to how the visual picture looks and views to him. What has been taught about remain same thing for the same purpose. What is different is how it has been explained, taught, preached, presented, painted, pictured, movied over the years. MAN'S effort in making it more clearer is gradually acheived by different men through different institute of  knowledge Eg Religious institute, Science and Technology institute, Institute Of Individualism. All committed to drive the universe(world) to the state we are now as a universe in general. Each and everyone of us benefit according to how clear the picture become to us which defines the importance of understandings common in the scripture and behold by the scientificism.. The scientist never give up in grasping more about the picture because the gradual little result is valued in order to sum up a huge factor of FAITH in their media of connectivity to the universe which serves as a cord between them and the universe.

Education is the study of universe. Do we understand why university is called "UNIVERSITY", its because its an institution meant to study about every bit of the universe but where African community misses most is the mother most course which is not encouraged here in Africa but it is encouraged in other parts of the continent like Europe, USA, China, Japan etc, of which every other thing were developed from its paramount and geniue ideas known to be "PHILOSOPHY". Let Africa generation focus on the study of the universe and create more ideas from it that will be useful for the coming generation to develop into "MATERIALISM" at a great pace and in no time, we will get there.
         Another useful ideology from Yoruba tribe that can be developed scientifically is quoted as follow
                              "OHUN TI A NWA LO SI SOKOTO, OWA LABE TABI NINU SOKOTO".

Which the Yoruba generation from time to time developed to compliment the immediate previous yourba quote above meaning in brief ,The solution is within our reach(within us). But there are still sub-ideas to develop more from these explained above. But if you follow the WESTERN ideas carefully that is related to these yoruba unfinished  pre-defined ideology quoted as follows
                                                    "WHAT IS WITHIN,IS WITHOUT"_western ideology

meaning it is well refined status whatever you want to materialise on the outside(your life,world,in a visible world, terrestial world) the key,the way out, the solution, the ideas, the guide etc is on the inside of you(within you). Further more,within your "HEART AND FEELING" where God visit as claimed by religious entities to know the request of MAN regardless the nature of the request and the contents of it. God even vowed clearly that it is from this media of heart and feeling that he will give to MAN according to his will.
My friend, understand that what you will and wish to yourself or to another man you have done,so therefore,
                                             HE says, "he will do to man according to what man does"SCripture
                         
                         "WHERE YOUR HEART IS, IS WHERE YOUR WEALTH IS"_The Alchemist.

So lets turn inward(minds) and think properly in the right(positive,good, etc.) manners,and ignore all the fables(negative,bad,etc.) manners.As an Africans where is your heart(mind)?, to develop yourself to develop your society?
There is more to understand about the power of philosophy and as time flies i will brief you on the continue parts in VOLUME.2 of "POWER OF PHILOSOPHY".

AFRICAN LETS BEGIN TO THINK THE FUTURE, SEE THE FUTURE ,PICTURE THE FUTURE,BUILD THE FUTURE AND LIVE THE FUTURE. BECAUSE OUR WORLD IS AFRICA AND WE ARE AFRICANS AND WE TURN IT AROUND. AFRICA DESTINATION IS IN OUR WILL. LETS WAKEUP AND GO OUT OF IGNORANCE AND TURN IT IN A RIGHT PATH REGARDING OUR WILL.YES I BELIEVE WE CAN,LETS GET READY.
                                                                          "A man who builds a house receives more honor than the house itself.In the same way jesus received more honor than moses"-hebrew.3:3.

Is of honor to us if given to us we materialise it. Lets join other race to rebuild what has been built in us through ideas to materialise for our comfortability. Wooooow!!!!!!!"--hebrew
                                                                                  "Every house, of course is built by someone----and GOD is the one who has built all things." hebrew 3:4.

GOD has built all things in heaven(inside) ,only inspire someone who aspires to rebuild it on earth(outside).According His will.
                 
                      "Let your will be done on         earth as it is done in heaven".---Jesus Christ.
                                                                   
  "I have studied the universe so much and the sceneros that surroud it,and i related it to history and scriptures,'God has created man to recreate himself' ". Wooow...what are we waiting for , Africans lets recreate ourselves to rebuid our society.
PROUDLY AFRICA,MY AFRICA.......

Thanks!!!!


PROUDLY AFRICA,

  LETS TURN IT, LETS MOVE IT,TO

TO A BEAUTY LIKE THIS,TO LIVE IN.



                                                               

THE POWER OF PHILOSOPHY.

By: busytimeweb on: July 30, 2019

9

ANSWERS TO KNOT X.

§ 1. The Chelsea Pensioners.

Problem.—If 70 per cent. have lost an eye, 75 per cent. an ear, 80 per cent. an arm, 85 per cent. a leg: what percentage, at least, must have lost all four?

Answer.—Ten.

Solution.—(I adopt that of Polar Star, as being better than my own). Adding the wounds together, we get 70 + 75 + 80 + 85 = 310, among 100 men; which gives 3 to each, and 4 to 10 men. Therefore the least percentage is 10.

Nineteen answers have been received. One is "5," but, as no working is given with it, it must, in accordance with the rule, remain "a deed without a name." Janet makes it "35 and ²⁄₁₀ths." I am sorry she has misunderstood the question, and has supposed that those who had lost an ear were 75 per cent. of those who had lost an eye; and so on. Of course, on this supposition, the percentages must all be multiplied together. This she has done correctly, but I can give her no honours, as I do not think the question will fairly bear her interpretation, Three Score and Ten makes it "19 and ²⁄₈ths." Her solution has given me—I will not say "many anxious days and sleepless nights," for I wish to be strictly truthful, but—some trouble in making any sense at all of it. She makes the number of "pensioners wounded once" to be 310 ("per cent.," I suppose!): dividing by 4, she gets 77 and a half as "average percentage:" again dividing by 4, she gets 19 and ²⁄₈ths as "percentage wounded four times." Does she suppose wounds of different kinds to "absorb" each other, so to speak? Then, no doubt, the data are equivalent to 77 pensioners with one wound each, and a half-pensioner with a half-wound. And does she then suppose these concentrated wounds to be transferable, so that ²⁄₄ths of these unfortunates can obtain perfect health by handing over their wounds to the remaining ¹⁄₄th? Granting these suppositions, her answer is right; or rather, if the question had been "A road is covered with one inch of gravel, along 77 and a half per cent. of it. How much of it could be covered 4 inches deep with the same material?" her answer would have been right. But alas, that wasn't the question! Delta makes some most amazing assumptions: "let every one who has not lost an eye have lost an ear," "let every one who has not lost both eyes and ears have lost an arm." Her ideas of a battle-field are grim indeed. Fancy a warrior who would continue fighting after losing both eyes, both ears, and both arms! This is a case which she (or "it?") evidently considers possible.

Next come eight writers who have made the unwarrantable assumption that, because 70 per cent. have lost an eye, therefore 30 per cent. have not lost one, so that they have both eyes. This is illogical. If you give me a bag containing 100 sovereigns, and if in an hour I come to you (my face not beaming with gratitude nearly so much as when I received the bag) to say "I am sorry to tell you that 70 of these sovereigns are bad," do I thereby guarantee the other 30 to be good? Perhaps I have not tested them yet. The sides of this illogical octagon are as follows, in alphabetical order:—Algernon Bray, Dinah Mite, G. S. C., Jane E., J. D. W., Magpie (who makes the delightful remark "therefore 90 per cent. have two of something," recalling to one's memory that fortunate monarch, with whom Xerxes was so much pleased that "he gave him ten of everything!"), S. S. G., and Tokio.

Bradshaw of the Future and T. R. do the question in a piecemeal fashion—on the principle that the 70 per cent. and the 75 per cent., though commenced at opposite ends of the 100, must overlap by at least 45 per cent.; and so on. This is quite correct working, but not, I think, quite the best way of doing it.

The other five competitors will, I hope, feel themselves sufficiently glorified by being placed in the first class, without my composing a Triumphal Ode for each!

CLASS LIST.

I.

Old Cat.
Old Hen.
Polar Star.
Simple Susan.
White Sugar.

II.

Bradshaw of the Future.
T. R.

III.

Algernon Bray.
Dinah Mite.
G. S. C.
Jane E.
J. D. W.
Magpie.
S. S. G.
Tokio.

§ 2. Change of Day.

I must postpone, sine die, the geographical problem—partly because I have not yet received the statistics I am hoping for, and partly because I am myself so entirely puzzled by it; and when an examiner is himself dimly hovering between a second class and a third how is he to decide the position of others?

§ 3. The Sons' Ages.

Problem.—"At first, two of the ages are together equal to the third. A few years afterwards, two of them are together double of the third. When the number of years since the first occasion is two-thirds of the sum of the ages on that occasion, one age is 21. What are the other two?

Answer.—"15 and 18."

Solution.—Let the ages at first be x, y, (x + y). Now, if a + b = 2c, then (a-n) + (b-n) = 2(c-n), whatever be the value of n. Hence the second relationship, if ever true, was always true. Hence it was true at first. But it cannot be true that x and y are together double of (x + y). Hence it must be true of (x + y), together with x or y; and it does not matter which we take. We assume, then, (x + y) + x = 2y; i.e. y = 2x. Hence the three ages were, at first, x, 2x, 3x; and the number of years, since that time is two-thirds of 6x, i.e. is 4x. Hence the present ages are 5x, 6x, 7x. The ages are clearly integers, since this is only "the year when one of my sons comes of age." Hence 7x = 21, x = 3, and the other ages are 15, 18.

Eighteen answers have been received. One of the writers merely asserts that the first occasion was 12 years ago, that the ages were then 9, 6, and 3; and that on the second occasion they were 14, 11, and 8! As a Roman father, I ought to withhold the name of the rash writer; but respect for age makes me break the rule: it is Three Score and Ten. Jane E. also asserts that the ages at first were 9, 6, 3: then she calculates the present ages, leaving the second occasion unnoticed. Old Hen is nearly as bad; she "tried various numbers till I found one that fitted all the conditions"; but merely scratching up the earth, and pecking about, is not the way to solve a problem, oh venerable bird! And close after Old Hen prowls, with hungry eyes, Old Cat, who calmly assumes, to begin with, that the son who comes of age is the eldest. Eat your bird, Puss, for you will get nothing from me!

There are yet two zeroes to dispose of. Minerva assumes that, on every occasion, a son comes of age; and that it is only such a son who is "tipped with gold." Is it wise thus to interpret "now, my boys, calculate your ages, and you shall have the money"? Bradshaw of the Future says "let" the ages at first be 9, 6, 3, then assumes that the second occasion was 6 years afterwards, and on these baseless assumptions brings out the right answers. Guide future travellers, an thou wilt: thou art no Bradshaw for this Age!

Of those who win honours, the merely "honourable" are two. Dinah Mite ascertains (rightly) the relationship between the three ages at first, but then assumes one of them to be "6," thus making the rest of her solution tentative. M. F. C. does the algebra all right up to the conclusion that the present ages are 5z, 6z, and 7z; it then assumes, without giving any reason, that 7z = 21.

Of the more honourable, Delta attempts a novelty—to discover which son comes of age by elimination: it assumes, successively, that it is the middle one, and that it is the youngest; and in each case it apparently brings out an absurdity. Still, as the proof contains the following bit of algebra, "63 = 7x + 4y; ∴ 21 = x + 4 sevenths of y," I trust it will admit that its proof is not quite conclusive. The rest of its work is good. Magpie betrays the deplorable tendency of her tribe—to appropriate any stray conclusion she comes across, without having any strict logical right to it. Assuming A, B, C, as the ages at first, and D as the number of the years that have elapsed since then, she finds (rightly) the 3 equations, 2A = B, C = B + A, D = 2B. She then says "supposing that A = 1, then B = 2, C = 3, and D = 4. Therefore for A, B, C, D, four numbers are wanted which shall be to each other as 1:2:3:4." It is in the "therefore" that I detect the unconscientiousness of this bird. The conclusion is true, but this is only because the equations are "homogeneous" (i.e. having one "unknown" in each term), a fact which I strongly suspect had not been grasped—I beg pardon, clawed—by her. Were I to lay this little pitfall, "A + 1 = B, B + 1 = C; supposing A = 1, then B = 2 and C = 3. Therefore for A, B, C, three numbers are wanted which shall be to one another as 1:2:3," would you not flutter down into it, oh Magpie, as amiably as a Dove? Simple Susan is anything but simple to me. After ascertaining that the 3 ages at first are as 3:2:1, she says "then, as two-thirds of their sum, added to one of them, = 21, the sum cannot exceed 30, and consequently the highest cannot exceed 15." I suppose her (mental) argument is something like this:—"two-thirds of sum, + one age, = 21; ∴ sum, + 3 halves of one age, = 31 and a half. But 3 halves of one age cannot be less than 1 and-a-half (here I perceive that Simple Susan would on no account present a guinea to a new-born baby!) hence the sum cannot exceed 30." This is ingenious, but her proof, after that, is (as she candidly admits) "clumsy and roundabout." She finds that there are 5 possible sets of ages, and eliminates four of them. Suppose that, instead of 5, there had been 5 million possible sets? Would Simple Susan have courageously ordered in the necessary gallon of ink and ream of paper?

The solution sent in by C. R. is, like that of Simple Susan, partly tentative, and so does not rise higher than being Clumsily Right.

Among those who have earned the highest honours, Algernon Bray solves the problem quite correctly, but adds that there is nothing to exclude the supposition that all the ages were fractional. This would make the number of answers infinite. Let me meekly protest that I never intended my readers to devote the rest of their lives to writing out answers! E. M. Rix points out that, if fractional ages be admissible, any one of the three sons might be the one "come of age"; but she rightly rejects this supposition on the ground that it would make the problem indeterminate. White Sugar is the only one who has detected an oversight of mine: I had forgotten the possibility (which of course ought to be allowed for) that the son, who came of age that year, need not have done so by that day, so that he might be only 20. This gives a second solution, viz., 20, 24, 28. Well said, pure Crystal! Verily, thy "fair discourse hath been as sugar"!

CLASS LIST.

I.

Algernon Bray.
An Old Fogey.
E. M. Rix.
G. S. C.
S. S. G.
Tokio.
T. R.
White Sugar.

II.

C. R.
Delta.
Magpie.
Simple Susan.

III.

Dinah Mite.
M. F. C.

I have received more than one remonstrance on my assertion, in the Chelsea Pensioners' problem, that it was illogical to assume, from the datum "70 p. c. have lost an eye," that 30 p. c. have not. Algernon Bray states, as a parallel case, "suppose Tommy's father gives him 4 apples, and he eats one of them, how many has he left?" and says "I think we are justified in answering, 3." I think so too. There is no "must" here, and the data are evidently meant to fix the answer exactly: but, if the question were set me "how many must he have left?", I should understand the data to be that his father gave him 4 at least, but may have given him more.

I take this opportunity of thanking those who have sent, along with their answers to the Tenth Knot, regrets that there are no more Knots to come, or petitions that I should recall my resolution to bring them to an end. I am most grateful for their kind words; but I think it wisest to end what, at best, was but a lame attempt. "The stretched metre of an antique song" is beyond my compass; and my puppets were neither distinctly in my life (like those I now address), nor yet (like Alice and the Mock Turtle) distinctly out of it. Yet let me at least fancy, as I lay down the pen, that I carry with me into my silent life, dear reader, a farewell smile from your unseen face, and a kindly farewell pressure from your unfelt hand! And so, good night! Parting is such sweet sorrow, that I shall say "good night!" till it be morrow.

THE END

***END OF A TANGLED TALE ***

9

By: busytimeweb on: July 29, 2019

8

CHAPTER 8

ANSWERS TO CORRESPONDENTS.

I have received several letters on the subjects of Knots II. and VI., which lead me to think some further explanation desirable.

In Knot II., I had intended the numbering of the houses to begin at one corner of the Square, and this was assumed by most, if not all, of the competitors. Trojanus however says "assuming, in default of any information, that the street enters the square in the middle of each side, it may be supposed that the numbering begins at a street." But surely the other is the more natural assumption?

In Knot VI., the first Problem was of course a mere jeu de mots, whose presence I thought excusable in a series of Problems whose aim is to entertain rather than to instruct: but it has not escaped the contemptuous criticisms of two of my correspondents, who seem to think that Apollo is in duty bound to keep his bow always on the stretch. Neither of them has guessed it: and this is true human nature. Only the other day—the 31st of September, to be quite exact—I met my old friend Brown, and gave him a riddle I had just heard. With one great effort of his colossal mind, Brown guessed it. "Right!" said I. "Ah," said he, "it's very neat—very neat. And it isn't an answer that would occur to everybody. Very neat indeed." A few yards further on, I fell in with Smith and to him I propounded the same riddle. He frowned over it for a minute, and then gave it up. Meekly I faltered out the answer. "A poor thing, sir!" Smith growled, as he turned away. "A very poor thing! I wonder you care to repeat such rubbish!" Yet Smith's mind is, if possible, even more colossal than Brown's.

The second Problem of Knot VI. is an example in ordinary Double Rule of Three, whose essential feature is that the result depends on the variation of several elements, which are so related to it that, if all but one be constant, it varies as that one: hence, if none be constant, it varies as their product. Thus, for example, the cubical contents of a rectangular tank vary as its length, if breadth and depth be constant, and so on; hence, if none be constant, it varies as the product of the length, breadth, and depth.

When the result is not thus connected with the varying elements, the Problem ceases to be Double Rule of Three and often becomes one of great complexity.

To illustrate this, let us take two candidates for a prize, A and B, who are to compete in French, German, and Italian:

(a) Let it be laid down that the result is to depend on their relative knowledge of each subject, so that, whether their marks, for French, be "1, 2" or "100, 200," the result will be the same: and let it also be laid down that, if they get equal marks on 2 papers, the final marks are to have the same ratio as those of the 3rd paper. This is a case of ordinary Double Rule of Three. We multiply A's 3 marks together, and do the same for B. Note that, if A gets a single "0," his final mark is "0," even if he gets full marks for 2 papers while B gets only one mark for each paper. This of course would be very unfair on A, though a correct solution under the given conditions.

(b) The result is to depend, as before, on relative knowledge; but French is to have twice as much weight as German or Italian. This is an unusual form of question. I should be inclined to say "the resulting ratio is to be nearer to the French ratio than if we multiplied as in (a), and so much nearer that it would be necessary to use the other multipliers twice to produce the same result as in (a):" e.g. if the French Ratio were ²⁄₁₀, and the others ²⁄₉, ¹⁄₉ so that the ultimate ratio, by method (a), would be ²⁄₄₅, I should multiply instead by ²⁄₃, ¹⁄₃, giving the result, ¹⁄₃ which is nearer to ²⁄₁₀ than if he had used method (a).

(c) The result is to depend on actual amount of knowledge of the 3 subjects collectively. Here we have to ask two questions. (1) What is to be the "unit" (i.e. "standard to measure by") in each subject? (2) Are these units to be of equal, or unequal value? The usual "unit" is the knowledge shown by answering the whole paper correctly; calling this "100," all lower amounts are represented by numbers between "0" and "100." Then, if these units are to be of equal value, we simply add A's 3 marks together, and do the same for B.

(d) The conditions are the same as (c), but French is to have double weight. Here we simply double the French marks, and add as before.

(e) French is to have such weight, that, if other marks be equal, the ultimate ratio is to be that of the French paper, so that a "0" in this would swamp the candidate: but the other two subjects are only to affect the result collectively, by the amount of knowledge shown, the two being reckoned of equal value. Here I should add A's German and Italian marks together, and multiply by his French mark.

But I need not go on: the problem may evidently be set with many varying conditions, each requiring its own method of solution. The Problem in Knot VI. was meant to belong to variety (a), and to make this clear, I inserted the following passage:

"Usually the competitors differ in one point only. Thus, last year, Fifi and Gogo made the same number of scarves in the trial week, and they were equally light; but Fifi's were twice as warm as Gogo's, and she was pronounced twice as good."

What I have said will suffice, I hope, as an answer to Balbus, who holds that (a) and (c) are the only possible varieties of the problem, and that to say "We cannot use addition, therefore we must be intended to use multiplication," is "no more illogical than, from knowledge that one was not born in the night, to infer that he was born in the daytime"; and also to Fifee, who says "I think a little more consideration will show you that our 'error of adding the proportional numbers together for each candidate instead of multiplying' is no error at all." Why, even if addition had been the right method to use, not one of the writers (I speak from memory) showed any consciousness of the necessity of fixing a "unit" for each subject. "No error at all!" They were positively steeped in error!

One correspondent (I do not name him, as the communication is not quite friendly in tone) writes thus:—"I wish to add, very respectfully, that I think it would be in better taste if you were to abstain from the very trenchant expressions which you are accustomed to indulge in when criticising the answer. That such a tone must not be" ("be not"?) "agreeable to the persons concerned who have made mistakes may possibly have no great weight with you, but I hope you will feel that it would be as well not to employ it, unless you are quite certain of being correct yourself." The only instances the writer gives of the "trenchant expressions" are "hapless" and "malefactors." I beg to assure him (and any others who may need the assurance: I trust there are none) that all such words have been used in jest, and with no idea that they could possibly annoy any one, and that I sincerely regret any annoyance I may have thus inadvertently given. May I hope that in future they will recognise the distinction between severe language used in sober earnest, and the "words of unmeant bitterness," which Coleridge has alluded to in that lovely passage beginning "A little child, a limber elf"? If the writer will refer to that passage, or to the preface to "Fire, Famine, and Slaughter," he will find the distinction, for which I plead, far better drawn out than I could hope to do in any words of mine.

The writer's insinuation that I care not how much annoyance I give to my readers I think it best to pass over in silence; but to his concluding remark I must entirely demur. I hold that to use language likely to annoy any of my correspondents would not be in the least justified by the plea that I was "quite certain of being correct." I trust that the knot-untiers and I are not on such terms as those!

I beg to thank G. B. for the offer of a puzzle—which, however, is too like the old one "Make four 9's into 100."

ANSWERS TO KNOT VIII.

§ 1. The Pigs.

Problem.—Place twenty-four pigs in four sties so that, as you go round and round, you may always find the number in each sty nearer to ten than the number in the last.

Answer.—Place 8 pigs in the first sty, 10 in the second, nothing in the third, and 6 in the fourth: 10 is nearer ten than 8; nothing is nearer ten than 10; 6 is nearer ten than nothing; and 8 is nearer ten than 6.

This problem is noticed by only two correspondents. Balbus says "it certainly cannot be solved mathematically, nor do I see how to solve it by any verbal quibble." Nolens Volens makes Her Radiancy change the direction of going round; and even then is obliged to add "the pigs must be carried in front of her"!

§ 2. The Grurmstipths.

Problem.—Omnibuses start from a certain point, both ways, every 15 minutes. A traveller, starting on foot along with one of them, meets one in 12½ minutes: when will he be overtaken by one?

Answer.—In 6¼ minutes.

Solution.—Let "a" be the distance an omnibus goes in 15 minutes, and "x" the distance from the starting-point to where the traveller is overtaken. Since the omnibus met is due at the starting-point in 2½ minutes, it goes in that time as far as the traveller walks in 12½; i.e. it goes 5 times as fast. Now the overtaking omnibus is "a" behind the traveller when he starts, and therefore goes "a + x" while he goes "x." Hence a + x = 5x; i.e. 4x = a, and x = a/4. This distance would be traversed by an omnibus in ¹⁵⁄₄ minutes, and therefore by the traveller in 5 × ¹⁵⁄₄. Hence he is overtaken in 18¾ minutes after starting, i.e. in 6¼ minutes after meeting the omnibus.

Four answers have been received, of which two are wrong. Dinah Mite rightly states that the overtaking omnibus reached the point where they met the other omnibus 5 minutes after they left, but wrongly concludes that, going 5 times as fast, it would overtake them in another minute. The travellers are 5-minutes-walk ahead of the omnibus, and must walk 1-4th of this distance farther before the omnibus overtakes them, which will be 1-5th of the distance traversed by the omnibus in the same time: this will require 1¼ minutes more. Nolens Volens tries it by a process like "Achilles and the Tortoise." He rightly states that, when the overtaking omnibus leaves the gate, the travellers are 1-5th of "a" ahead, and that it will take the omnibus 3 minutes to traverse this distance; "during which time" the travellers, he tells us, go 1-15th of "a" (this should be 1-25th). The travellers being now 1-15th of "a" ahead, he concludes that the work remaining to be done is for the travellers to go 1-60th of "a," while the omnibus goes l-12th. The principle is correct, and might have been applied earlier.

CLASS LIST.

I.

Balbus.
Delta.

ANSWERS TO KNOT IX.

§ 1. The Buckets.

Problem.—Lardner states that a solid, immersed in a fluid, displaces an amount equal to itself in bulk. How can this be true of a small bucket floating in a larger one?

Solution.—Lardner means, by "displaces," "occupies a space which might be filled with water without any change in the surroundings." If the portion of the floating bucket, which is above the water, could be annihilated, and the rest of it transformed into water, the surrounding water would not change its position: which agrees with Lardner's statement.

Five answers have been received, none of which explains the difficulty arising from the well-known fact that a floating body is the same weight as the displaced fluid. Hecla says that "only that portion of the smaller bucket which descends below the original level of the water can be properly said to be immersed, and only an equal bulk of water is displaced." Hence, according to Hecla, a solid, whose weight was equal to that of an equal bulk of water, would not float till the whole of it was below "the original level" of the water: but, as a matter of fact, it would float as soon as it was all under water. Magpie says the fallacy is "the assumption that one body can displace another from a place where it isn't," and that Lardner's assertion is incorrect, except when the containing vessel "was originally full to the brim." But the question of floating depends on the present state of things, not on past history. Old King Cole takes the same view as Hecla. Tympanum and Vindex assume that "displaced" means "raised above its original level," and merely explain how it comes to pass that the water, so raised, is less in bulk than the immersed portion of bucket, and thus land themselves—or rather set themselves floating—in the same boat as Hecla.

I regret that there is no Class-list to publish for this Problem.

§ 2. Balbus' Essay.

Problem.—Balbus states that if a certain solid be immersed in a certain vessel of water, the water will rise through a series of distances, two inches, one inch, half an inch, &c., which series has no end. He concludes that the water will rise without limit. Is this true?

Solution.—No. This series can never reach 4 inches, since, however many terms we take, we are always short of 4 inches by an amount equal to the last term taken.

Three answers have been received—but only two seem to me worthy of honours.

Tympanum says that the statement about the stick "is merely a blind, to which the old answer may well be applied, solvitur ambulando, or rather mergendo." I trust Tympanum will not test this in his own person, by taking the place of the man in Balbus' Essay! He would infallibly be drowned.

Old King Cole rightly points out that the series, 2, 1, &c., is a decreasing Geometrical Progression: while Vindex rightly identifies the fallacy as that of "Achilles and the Tortoise."

CLASS LIST.

I.

Old King Cole.
Vindex.

§ 3. The Garden.

Problem.—An oblong garden, half a yard longer than wide, consists entirely of a gravel-walk, spirally arranged, a yard wide and 3,630 yards long. Find the dimensions of the garden.

Answer.—60, 60½.

Solution.—The number of yards and fractions of a yard traversed in walking along a straight piece of walk, is evidently the same as the number of square-yards and fractions of a square-yard, contained in that piece of walk: and the distance, traversed in passing through a square-yard at a corner, is evidently a yard. Hence the area of the garden is 3,630 square-yards: i.e., if x be the width, x (x + ½) = 3,630. Solving this Quadratic, we find x = 60. Hence the dimensions are 60, 60½.

Twelve answers have been received—seven right and five wrong.

C. G. L., Nabob, Old Crow, and Tympanum assume that the number of yards in the length of the path is equal to the number of square-yards in the garden. This is true, but should have been proved. But each is guilty of darker deeds. C. G. L.'s "working" consists of dividing 3,630 by 60. Whence came this divisor, oh Segiel? Divination? Or was it a dream? I fear this solution is worth nothing. Old Crow's is shorter, and so (if possible) worth rather less. He says the answer "is at once seen to be 60 × 60½"! Nabob's calculation is short, but "as rich as a Nabob" in error. He says that the square root of 3,630, multiplied by 2, equals the length plus the breadth. That is 60.25 × 2 = 120½. His first assertion is only true of a square garden. His second is irrelevant, since 60.25 is not the square-root of 3,630! Nay, Bob, this will not do! Tympanum says that, by extracting the square-root of 3,630, we get 60 yards with a remainder of 30/60, or half-a-yard, which we add so as to make the oblong 60 × 60½. This is very terrible: but worse remains behind. Tympanum proceeds thus:—"But why should there be the half-yard at all? Because without it there would be no space at all for flowers. By means of it, we find reserved in the very centre a small plot of ground, two yards long by half-a-yard wide, the only space not occupied by walk." But Balbus expressly said that the walk "used up the whole of the area." Oh, Tympanum! My tympa is exhausted: my brain is num! I can say no more.

Hecla indulges, again and again, in that most fatal of all habits in computation—the making two mistakes which cancel each other. She takes x as the width of the garden, in yards, and x + ½ as its length, and makes her first "coil" the sum of x½, x½, x-1, x-1, i.e. 4x-3: but the fourth term should be x-1½, so that her first coil is ½ a yard too long. Her second coil is the sum of x-2½, x-2½, x-3, x-3: here the first term should be x-2 and the last x-3½: these two mistakes cancel, and this coil is therefore right. And the same thing is true of every other coil but the last, which needs an extra half-yard to reach the end of the path: and this exactly balances the mistake in the first coil. Thus the sum total of the coils comes right though the working is all wrong.

Of the seven who are right, Dinah Mite, Janet, Magpie, and Taffy make the same assumption as C. G. L. and Co. They then solve by a Quadratic. Magpie also tries it by Arithmetical Progression, but fails to notice that the first and last "coils" have special values.

Alumnus Etonæ attempts to prove what C. G. L. assumes by a particular instance, taking a garden 6 by 5½. He ought to have proved it generally: what is true of one number is not always true of others. Old King Cole solves it by an Arithmetical Progression. It is right, but too lengthy to be worth as much as a Quadratic.

Vindex proves it very neatly, by pointing out that a yard of walk measured along the middle represents a square yard of garden, "whether we consider the straight stretches of walk or the square yards at the angles, in which the middle line goes half a yard in one direction and then turns a right angle and goes half a yard in another direction."

CLASS LIST.

I.

Vindex.

II.

Alumnus Etonæ.
Old King Cole.

III.

Dinah Mite.
Janet.
Magpie.
Taffy.

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8

By: busytimeweb on: July 29, 2019